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Popular Calculus Problems

(dy)/(dx)=(x-18)^2	\frac{dy}{dx}=(x-18)^{2}
limit as x approaches 4 of 9/x	\lim\:_{x\to\:4}(\frac{9}{x})
inverse oflaplace (2s)/((s^2+25)(s-1))	inverselaplace\:\frac{2s}{(s^{2}+25)(s-1)}
derivative of y=(2x)/(x^2-1)	derivative\:y=\frac{2x}{x^{2}-1}
derivative of y(θ)=e^{tan(θ)}	derivative\:y(θ)=e^{\tan(θ)}
area y=2-x^2,y=x	area\:y=2-x^{2},y=x
limit as x approaches-2 of (-5x-10)/(x^3+2x^2)	\lim\:_{x\to\:-2}(\frac{-5x-10}{x^{3}+2x^{2}})
derivative of (6x)/(sqrt(x^2+2))	derivative\:\frac{6x}{\sqrt{x^{2}+2}}
(dy)/(dx)= 1/(xsqrt(16x^2-1))	\frac{dy}{dx}=\frac{1}{x\sqrt{16x^{2}-1}}
derivative of f(x)=(x^2-4)(x+1)	derivative\:f(x)=(x^{2}-4)(x+1)
area 4x,x^2-12	area\:4x,x^{2}-12
t^2y^{''}+7ty^'+5y=0	t^{2}y^{\prime\:\prime\:}+7ty^{\prime\:}+5y=0
derivative of x^2-sqrt(x)+5	\frac{d}{dx}(x^{2}-\sqrt{x}+5)
integral from 1 to 4 of 1/(x^2)	\int\:_{1}^{4}\frac{1}{x^{2}}dx
derivative of sin(x-1/18 sin(3x))	\frac{d}{dx}(\sin(x)-\frac{1}{18}\sin(3x))
derivative of 1/((1+x^2))	derivative\:\frac{1}{(1+x^{2})}
derivative of (x+2^{2x-3})	\frac{d}{dx}((x+2)^{2x-3})
d/(dt)(e^{-it})	\frac{d}{dt}(e^{-it})
limit as x approaches 6 of cx^2+9x	\lim\:_{x\to\:6}(cx^{2}+9x)
(\partial}{\partial u}(\frac{v-u)/2)	\frac{\partial\:}{\partial\:u}(\frac{v-u}{2})
slope of (-3,-8),(5,6)	slope\:(-3,-8),(5,6)
(\partial)/(\partial x)(x^2y+2y^2-6x+3y-4)	\frac{\partial\:}{\partial\:x}(x^{2}y+2y^{2}-6x+3y-4)
integral of 2/(sqrt(1-x^2))	\int\:\frac{2}{\sqrt{1-x^{2}}}dx
d/(d{y)}(e^{{y}{z}})	\frac{d}{d{y}}(e^{{y}{z}})
derivative of f(x)=x^3(3x-5)^2	derivative\:f(x)=x^{3}(3x-5)^{2}
integral from 1 to 2 of 6/(x^2)	\int\:_{1}^{2}\frac{6}{x^{2}}dx
integral from-3 to 3 of (2-\|x\|)	\int\:_{-3}^{3}(2-\left\|x\right\|)dx
derivative of sqrt(x^6)	\frac{d}{dx}(\sqrt{x^{6}})
derivative of (2x-sqrt(x)(5x+2))	\frac{d}{dx}((2x-\sqrt{x})(5x+2))
integral of (sin^2(x))/(cos^4(x))	\int\:\frac{\sin^{2}(x)}{\cos^{4}(x)}dx
sum from n=0 to infinity of e^{-0.06n}	\sum\:_{n=0}^{\infty\:}e^{-0.06n}
y^{''}-5y^'+6y=2e^{t/2}	y^{\prime\:\prime\:}-5y^{\prime\:}+6y=2e^{\frac{t}{2}}
derivative of csc^7(2x^pi+pi^3)	\frac{d}{dx}(\csc^{7}(2x^{π}+π^{3}))
area sin^2(x),sin^4(x),[0,pi]	area\:\sin^{2}(x),\sin^{4}(x),[0,π]
integral of (4x+1)sqrt(x-5)	\int\:(4x+1)\sqrt{x-5}dx
(dy)/(dx)=3cos(7x)	\frac{dy}{dx}=3\cos(7x)
derivative of g(x)=sqrt(x)+5	derivative\:g(x)=\sqrt{x}+5
integral of 4x-2sqrt(x)	\int\:4x-2\sqrt{x}dx
integral of e^2ln(x)	\int\:e^{2}\ln(x)dx
integral of x/(sqrt(1-9x^2))	\int\:\frac{x}{\sqrt{1-9x^{2}}}dx
limit as x approaches 4 of (\|4-x\|)/(4-x)	\lim\:_{x\to\:4}(\frac{\left\|4-x\right\|}{4-x})
integral of (2x^{-1})	\int\:(2x^{-1})dx
2y^{''}+y^'-3y=0	2y^{\prime\:\prime\:}+y^{\prime\:}-3y=0
integral of (2x-5)^3	\int\:(2x-5)^{3}dx
y^'= y/(4x)	y^{\prime\:}=\frac{y}{4x}
(\partial)/(\partial x)(2x^2+3y^2-20)	\frac{\partial\:}{\partial\:x}(2x^{2}+3y^{2}-20)
derivative of sqrt(y/3)	derivative\:\sqrt{\frac{y}{3}}
integral from 0 to (3pi)/2 of 9\|sin(x)\|	\int\:_{0}^{\frac{3π}{2}}9\left\|\sin(x)\right\|dx
integral of (e^{2x})/(-2)	\int\:\frac{e^{2x}}{-2}dx
integral from 0 to infinity of 1/(9+x^2)	\int\:_{0}^{\infty\:}\frac{1}{9+x^{2}}dx
integral of 1/((x^2+2x))	\int\:\frac{1}{(x^{2}+2x)}dx
derivative of x^2-x^3+4	derivative\:x^{2}-x^{3}+4
limit as x approaches infinity of x^3-1	\lim\:_{x\to\:\infty\:}(x^{3}-1)
(\partial)/(\partial x)(sqrt(x^2+y^2)-x)	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+y^{2}}-x)
y^'=-((2x+ln(y))y)/x	y^{\prime\:}=-\frac{(2x+\ln(y))y}{x}
derivative of y=x^2sin(pix)	derivative\:y=x^{2}\sin(πx)
(\partial)/(\partial x)(-5x^2-2xy-3y^2)	\frac{\partial\:}{\partial\:x}(-5x^{2}-2xy-3y^{2})
derivative of arccot(x/9)	derivative\:\arccot(\frac{x}{9})
integral of (sqrt(x)-1)/(sqrt(x)+1)	\int\:\frac{\sqrt{x}-1}{\sqrt{x}+1}dx
integral of (2x+3)/((x+1)^2)	\int\:\frac{2x+3}{(x+1)^{2}}dx
implicit 8x^2+7y^2=56	implicit\:8x^{2}+7y^{2}=56
derivative of (x^2/(2(1-x)))	\frac{d}{dx}(\frac{x^{2}}{2(1-x)})
(\partial)/(\partial y)((x^3+2y^2)^3)	\frac{\partial\:}{\partial\:y}((x^{3}+2y^{2})^{3})
f(x)=(cot(x))/(1+cot(x))	f(x)=\frac{\cot(x)}{1+\cot(x)}
(1+e^t)y^'+e^ty=0	(1+e^{t})y^{\prime\:}+e^{t}y=0
integral of (e^{1/t})/(t^3)	\int\:\frac{e^{\frac{1}{t}}}{t^{3}}dt
derivative of e^y	derivative\:e^{y}
integral of cos(x)(2+sin(x))^5	\int\:\cos(x)(2+\sin(x))^{5}dx
limit as x approaches 0 of x^2+2x-2	\lim\:_{x\to\:0}(x^{2}+2x-2)
(\partial)/(\partial x)(e^xln(1+y))	\frac{\partial\:}{\partial\:x}(e^{x}\ln(1+y))
(x+1)(dy)/(dx)+y=ln(x),y(1)=10	(x+1)\frac{dy}{dx}+y=\ln(x),y(1)=10
(\partial)/(\partial x)(7ye^{5x})	\frac{\partial\:}{\partial\:x}(7ye^{5x})
area y=ln(x),y=0,x=4e	area\:y=\ln(x),y=0,x=4e
roots sin(ax)	roots\:\sin(ax)
integral of ((1-3x))/(sqrt(2x-3x^2))	\int\:\frac{(1-3x)}{\sqrt{2x-3x^{2}}}dx
derivative of-2/(x^2+1)	\frac{d}{dx}(-\frac{2}{x^{2}+1})
(dy)/(dx)=((x-3))/((y+1))	\frac{dy}{dx}=\frac{(x-3)}{(y+1)}
derivative of f(x)= 1/((1+x^2))	derivative\:f(x)=\frac{1}{(1+x^{2})}
derivative of (x^2-3x+2)/(-x^2-4x-4)	derivative\:\frac{x^{2}-3x+2}{-x^{2}-4x-4}
(\partial)/(\partial x)(ln(sin(x)))	\frac{\partial\:}{\partial\:x}(\ln(\sin(x)))
integral of x^2(x^3+1)^3	\int\:x^{2}(x^{3}+1)^{3}dx
integral of (x^2+x)e^{-2x}	\int\:(x^{2}+x)e^{-2x}dx
(dy)/(dx)=(x^2-y^2)/(xy),y(2)=2	\frac{dy}{dx}=\frac{x^{2}-y^{2}}{xy},y(2)=2
area 4x,x^2-5	area\:4x,x^{2}-5
integral of sex(x)	\int\:sex(x)
area f(x)=x^2-4,1,3	area\:f(x)=x^{2}-4,1,3
slope of y= 7/(sqrt(x))	slope\:y=\frac{7}{\sqrt{x}}
integral from 0 to infinity of 12e^{-6x}	\int\:_{0}^{\infty\:}12e^{-6x}dx
integral of (4sqrt(x^2+16))/(x^4)	\int\:\frac{4\sqrt{x^{2}+16}}{x^{4}}dx
integral of-sec^2((7x)/6)	\int\:-\sec^{2}(\frac{7x}{6})dx
sum from n=4 to infinity of 6/(n^2-1)	\sum\:_{n=4}^{\infty\:}\frac{6}{n^{2}-1}
limit as x approaches 0 of e^{-x(1-s)}	\lim\:_{x\to\:0}(e^{-x(1-s)})
limit as x approaches pi of sin(x)	\lim\:_{x\to\:π}(\sin(x))
tangent of f(x)=5sin(x)-3cos(x),\at x=pi	tangent\:f(x)=5\sin(x)-3\cos(x),\at\:x=π
integral of 5xe^{8x}	\int\:5xe^{8x}dx
integral of (e^x)/(e^x+2)	\int\:\frac{e^{x}}{e^{x}+2}dx
derivative of (5-3x/(x^2+3x))	\frac{d}{dx}(\frac{5-3x}{x^{2}+3x})
tangent of cos((pix)/2)	tangent\:\cos(\frac{πx}{2})
integral from 0 to 1 of 4xarccos(x)	\int\:_{0}^{1}4x\arccos(x)dx
integral of (13x^3)/(sqrt(2+x^2))	\int\:\frac{13x^{3}}{\sqrt{2+x^{2}}}dx

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